I think that a good finale season needs to bring the show back to its roots, really grab ahold of what that show is all about, and keep that theme strong throughout the season. It really does need to go back to basics. But at the same time, it really needs to take all the characters to new places. Their stories and arcs need to be wrapped up, and they need to be taken to a next step in their lives. There must be a cohesion between continuity and progress, a sense that all the characters have changed and evolved and gone through all sorts of trials and tribulations, but that they've come out stronger.
Season Five of Buffy was, I think, the absolute perfect season. All the characters had significant development and entered a new stage of their life in some way or another. Buffy was thrust into the adult world and made to cope as an authority figure, and discovered more about her roots as a slayer, and what that means for her and her destiny (which, by the way, was captured beautifully in her sacrifice scene, where she completely rejected the supposed inevitability of her dying alone and scared, offed by some random vamp in a back alley, and instead chose to die in a selfless act of heroism, saving her sister, her friends, and the world - and then the close in on the tombstone with the absolute perfect message, that just strips right to the core and, no-nonsense, lays out exactly who Buffy was. But I digress...)
Xander found success and purpose at last with his career, a kind of confidence in The Replacement, and got over his fear of commitment by proposing to Anya. Willow became more serious with Tara and entered a new stage of power as her magic grew in strength. Giles found a new purpose and regained his self-respect with taking over The Magic Box (and of course was reinstated in his rightful place as Buffy's watcher, a nice back-to-basics touch there). Anya made peace with her humanity and mortality. Tara started to grow out of her shell and found real love and acceptance with Willow. Spike discovered a human side of himself with his newfound love for Buffy.
Yet in spite of all the changes, when it all came down to it they were just the same as they always had been, fighting evil side by side. All of the tensions and distance between them that had grown in S4 were repaired, the personal demons were conquered. They had been beaten, broken, hunted down and stripped to the core, but they came out of it fighting, together.
Season 7 I believe does it all wrong. They did alright at first - there was a strong back-to-basics theme in the opening episodes, a good mending of the broken bonds between the characters, decent focus on all characters... but about 8 episodes in it all went to pot. When the show should be focusing on the original characters, and giving fair development to all others, the focus was split and skewed. Unnecessary additional characters like Andrew, Wood, Kennedy and the rest of the potentials obscured the characters we'd been with since the beginning, and of course the excessive focus on Spike was of great damage. Most of the characters suffer greatly from this - Willow's arc is weak at best, and Xander, Giles, Dawn and Anya (post-Selfless) don't get any development whatsoever.
Important bonds like Buffy and Giles' are destroyed and then never repaired. The bonds between the core scoobies just don't exist for most of S7. These monumentally important, close-knit friendships become an afterthought. The characters drift apart and change too much. You can really see this in the "The Earth is doomed" scene in Chosen that calls back to Welcome to the Hellmouth. It's a shoddy, half-assed afterthought of a back-to-basics theme, and it doesn't work at all because, unlike the original, it doesn't feel natural. The characters have changed too much and their bonds have been so neglected that a sudden reversion to exactly how they acted with each other in S1 seems sudden and forced. There should be a return to the roots of the show, but not in a way that acts as though nothing's happened in the last 7 years.
And of course, while S5 ends with every character fighting together and each having an important role to play, S7 ends with most of the characters being an afterthought, with Xander and Giles having essentially the same role as Andrew and Wood (by the way, not criticising these characters, but they are nowhere near as important to the series as Xander and Giles, and so shouldn't get the same attention). And of course everyone gets obscured by the legions of nu-slayers that nobody cares about. While S5 ends with Buffy, the main character and heroine of the series, heroically saving the world, S7 ends with Spike, a promoted minor villain, heroically saving the world. Say what you like about Spike, good or bad, I'm just saying that the climax of the entire series should be dedicated to the girl that the series is all about, not a supporting character that was supposed to be killed off after his fifth appearance.
S5 I think also suffers greatly from moving too far away from its roots. I'm not going to go into details about my thoughts because it's nearing two in the morning here and, lets face it, you're getting bored of this post. I think the closing episodes should have been about what the show was supposed to be about right from the start, Angel's suppsoed mission; helping the helpless. The "assassinate an evil cult" plot was too far removed from the show's orginal ethos. It should be more about protecting the innocent, and less about chasing after the guilty. And again, I think that there should've been more of a focus on the original cast. In that closing shot, we had Angel, Gunn, and two characters that had only recently been introduced to the show and neither of whom were ever a real part of the group.
tl;dr = The Gift rocks, everything else sucks.